I can also use app.call("Quit") and it closes Illustrator, but I can not use doc.call("Close") which should close the opened EPS. So, somehow I can execute any head or top object, but not any sub-object.

Thanks John. After a few tries with downloading 0.3, it would still not work. And so I said, maybe he meant 0.3.5 and I downloaded it and TA-DAAAAH! It works. Here is the program now, for completion of thread: